One of the amazing things about science is how often things at one scale apply at another as well. For example, you can measure the way that a cup of lye reacts with a cup of water and know how much heat will be produced if you use a ton of lye and a ton of water instead. Or you can simulate an earthquake using a piece of spaghetti and that will teach you something about how the San Andreas behaves. Or, as Peter and Mary are about to discover, you can use a pile of rice to discover why the Earth is round.
The images on the television were both frightening and fascinating. There had been a heavy rainfall in California and the runoff was rapidly eroding the base of a cliff, causing parts of the cliff to collapse in large chunks that splashed mud and mayhem when they fell. That would have been fascinating enough but on top of the cliff were several multi-million dollar mansions that were following the formerly stable cliff on its downward plunge.
“Wow!” said Peter as he watched a particularly large chunk of a swimming pool fall twenty stories into the surf below. “That was amazing!”
“Yes,” agreed Mary. “I’m glad that they got all of the people out. But what about their stuff?”
“I guess they’ve got insurance,” Peter replied. “But why did they build on the cliff?”
“Probably for the view. But what I want to know is why isn’t the cliff still still standing?” Mary puzzled. “It was doing OK before the rain, so why fall now?”
“I dunno. Who could we ask?” Peter wondered.
“Well, Mr. Medes is on vacation this week, so we can’t ask him,” Mary said. “And your mom is an astronomer, so she wouldn’t know. That just leave my dad. But he’s an engineer. He probably won’t know either.”
“Well, there’s only one way to find out,” Peter said. “Let’s go ask him!”
With that the two young scientists left the den where they had been watching television and sought out Mary’s father. Since it was Saturday, the first place they checked was the kitchen; in addition to being a popular engineering professor at the local university, he was also an amateur gourmet chef who liked to make special meals on weekends. Sure enough, he was in front of the stove, cooking raw rice in oil and fragrant spices.
“Oh, boy!” Mary exclaimed. “Costless Rican Rice again?”
“You betcha!” her father replied. “I wanted to use up the last of that roast chicken and we had enough vegetables to make this interesting. Peter, would you like to stay for dinner?”
“I’ll ask my mom,” Peter said as his belly rumbled in response to the smell of the cooking. Mary’s father laughed at the sound.
“It sounds as if your stomach has already decided the answer will be ‘yes'”, he said as he stirred the rice. “So what may I do to help you two? Or are you just drawn to the sight of a master turning leftovers into a meal fit for a king?”
“We had a question about cliffs,” Mary said. “Why do they fall down?”
“That is an excellent question!” Her father boomed in response. “And I’ll tell you the answer just as soon as I toss these odds and ends into the rice.”
With that, Mary’s father scrapped chunks of cooked chicken and vegetables that were left over from the previous week’s meals into the rice. Pouring in a carefully measured amount of water, he gave the mass a final stir and put a lid on top. He then turned the heat down and turned to his daughter and her friend.
“So you want to know why cliffs fall down,” he said. “Why do you ask?”
“Well, we saw these cliffs in California that were falling apart and dragging the houses that were on top of them into the mud,” Mary said. “But the cliffs were only about two hundred feet tall. We’ve got skyscrapers that are ten times as tall. So why do the skyscrapers stand up and the cliffs fall down?”
“It turns out that you have come to exactly the right person to answer that question,” her father replied. “Though Peter’s mother might have done just as well; this applies to her field as well.”
“It does?” Peter asked. “How?”
“You’ll see!” Mary’s father replied. “To start with, we’ll need a couple of plates, some toothpicks, and some uncooked rice.”
Mary quickly went to the pantry and grabbed the things that her father had listed off. Her father took the plates from her and placed on in front of each of the scientists. He then gave them each a toothpick and poured a cupful of rice onto each plate.
“In front of each of you is a pile of rice,” he said. “What I want you to do is to make the tallest cliff of rice that you can by scraping away the rice at the bottom of the pile with the toothpick. When you are done, what do you think the cliff will look like?”
“It will be just like a real cliff,” Peter confidently said. “It will go straight up.”
“I’m no so sure,” Mary countered. “I think it will be a lot slope-ier. It will probably lean over more.”
“Well, there’s only one way to find out,” her father said. “Start scraping!”
What do you think will happen? Try the experiment yourself!
The two started scraping at the base of their rice piles. But as soon as they would start to build up a small cliff, the bottom would slide out and a small cascade of rice would flow down, turning the vertical wall into a horizontal slope. After a few minutes of diligent scraping, Peter tossed down his toothpick in disgust.
“I give up!” he declared. “The rice won’t make a cliff! It is even worse than what we saw on TV!”
“Peter’s right,” Mary agreed. “You can’t make a tall cliff out of rice.”
“You are both right,” her father said. “You can’t make a tall cliff out of rice and you can’t make a skyscraper out of sand. And in both cases, the reason is the same.”
“It is?” Mary asked.
“Yes,” her father replied. “What is happening is that every stack of stuff is a balance of two things. There is gravity, which is pushing down on all the parts of it and there is cohesiveness which is trying to keep everything together. When gravity pushed on the center of a pile of rice or a cliff or a skyscraper, the force is straight down. That creates pressure on the grains of rice which gets bigger as you go deeper into the pile. The rice on top feels very little pressure while the rice at the bottom feels a lot. If the pressure on a grain of rice is about the same as the pressure on the grains around it, everything is stable and nothing moves. But if the pressure is lower on one side, then things naturally try to move in that direction. And when the difference in pressure is greater than the cohesiveness, then -“
“You get a landslide!” Mary exclaimed.
“That’s right!” her father agreed. “If you watched carefully during your experiment, then you probably saw that the rice-slides only happened on the side where you were scraping. That was because that was the only side where the pressure was changing.”
“Oh!” Peter said with a look of sudden understanding. “And that’s why the cliffs were falling. When the water eroded enough of the base, the pressure from the dirt piled up in the cliff was more than the strength of the stuff holding the cliff together and – pow! – we got a landslide!”
“That’s right. And that should also tell you why you can’t build a twenty story cliff of rice or a two hundred story cliff of sand,” Mary’s father said.
“Because rice isn’t as strong as sand and that’s not as strong as the steel in a skyscraper!” Mary said. “But why could Peter’s mother have told us this, too?”
“Because she works with planets,” her father replied. “And the one part of the definition of a planet that everyone agrees on is that they are round thanks to their own gravity.”
“I don’t get it,” Peter said.
“Imagine that you are building a cliff of sand,” Mary’s father said. “What happens if it gets too tall?”
“Some of it collapses,” Peter said.
“OK, now imagine that you’ve got a pile of sand as big as a planet,” Mary’s father said. “What happens to that cliff?”
“It will collapse,” Mary said.
“And if the cliffs that creates are too tall?”
“Then they will collapse too,” Peter said.
“And what happens if you keep doing that all around the planet-sized sand pile?” Mary father asked.
“I get it!” Mary said. “No matter where you look, the sand piles can only be so tall. And that means that everywhere you look, everything is about the same distance from the center of the planet. And that makes it -“
“Round!” Peter and Mary chorused together.
“That’s right,” Mary’s father said. “And now, if you two will clean up your budding planets and if Peter will call his mother, we can eat dinner.”
With that reminder, Peter’s stomach once more rumbled threateningly and all three laughed as they set the table for dinner.